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A circular disk of moment of inertia $I_t$ is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed $\omega_i$. Another disk of moment of inertia $I_b$ is dropped coaxially onto the rotating disk. Initially the second disk has zero angular speed. Eventually both the disks rotate with a constant angular speed $\omega_f$. The energy lost by the initially rotating disc to friction is:
What would be the torque about the origin when a force $3\hat{j} \text{ N}$ acts on a particle whose position vector is $2\hat{k} \text{ m}$?
A system consists of three masses $m_1$, $m_2$ and $m_3$ connected by a string passing over a pulley P. The mass $m_1$ hangs freely and $m_2$ and $m_3$ are on a rough horizontal table (the coefficient of friction = $\mu$). The pulley is frictionless and of negligible mass. The downward acceleration of mass $m_1$ is: (Assume $m_1=m_2=m_3=m$)
A force $\vec{F} = \alpha\hat{i} + 3\hat{j} + 6\hat{k}$ is acting at a point $\vec{r} = 2\hat{i} - 6\hat{j} - 12\hat{k}$. The value of $\alpha$ for which angular momentum is conserved about the origin is:
The upper half of an inclined plane of inclination $\theta$ is perfectly smooth while the lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom if the coefficient of friction between the block and lower half of the plane is given by:
From a disc of radius $R$ and mass $M$, a circular hole of diameter $R$, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the centre?
A string is wrapped along the rim of a wheel of the moment of inertia $0.10 \text{ kg-m}^2$ and radius $10 \text{ cm}$. If the string is now pulled by a force of $10 \text{ N}$, then the wheel starts to rotate about its axis from rest. The angular velocity of the wheel after $2 \text{ s}$ will be:
The angular acceleration of a body moving along the circumference of a circle is:
A person of mass $60 \text{ kg}$ is inside a lift of mass $940 \text{ kg}$ and presses the button on the control panel. The lift starts moving upwards with an acceleration of $1.0 \text{ m/s}^2$. If $g=10 \text{ m/s}^2$, the tension in the supporting cable is:
Consider a thin circular ring (A), a circular disc (B), a hollow cylinder (C) and a solid cylinder (D) of the same radii $R$ and of the same masses. If $I_A$, $I_B$, $I_C$ and $I_D$ are their moments of inertia about the axis shown, then choose the correct answer from the options given below:
If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is:
A particle of mass $m$ and charge $(-q)$ enters the region between the two charged plates initially moving along the x-axis with speed $v_x$ (as shown in the figure). The length of the plate is $L$ and a uniform electric field $E$ is maintained between the plates. The vertical deflection of the particle at the far edge of the plate is:
Liquid oxygen at $50 \text{ K}$ is heated up to $300 \text{ K}$ at a constant pressure of $1 \text{ atm}$. The rate of heating is constant. Which one of the following graphs represents the variation of temperature with time?
A black body at $1227^\circ\text{C}$ emits radiations with maximum intensity at a wavelength of $5000 \text{ \AA}$. If the temperature of the body is increased by $1000^\circ\text{C}$, the maximum intensity will be observed at:
A rigid ball of mass $M$ strikes a rigid wall at $60^{\circ}$ and gets reflected without loss of speed, as shown in the figure. The value of the impulse imparted by the wall on the ball will be:
The force $F$ acting on a particle of mass $m$ is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from $0$ to $8$ s is:
A rod PQ of mass $M$ and length $L$ is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in the figure. When the string is cut, the initial angular acceleration of the rod is:
A solid sphere of mass $m$ and radius $R$ is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation ($E_{\text{sphere}}/E_{\text{cylinder}}$) will be:
A particle moving with velocity $\vec{v}$ is acted by three forces shown by the vector triangle $PQR$. The velocity of the particle will:
A wheel is subjected to uniform angular acceleration about its axis. Initially, its angular velocity is zero. In the first $2\text{ s}$, it rotates through an angle $\theta_1$. In the next $2\text{ s}$, it rotates through an additional angle $\theta_2$. The ratio of $\frac{\theta_2}{\theta_1}$ is: